Braided m-Lie algebras induced by multiplication are introduced, which generalize Lie algebras, Lie color algebras and quantum Lie algebras. The necessary and sufficient conditions for the braided m-Lie algebras to be strict Jacobi braided Lie algebras are given. Two classes of braided m-Lie algebras are given, which are generalized matrix braided m-Lie algebras and braided m-Lie subalgebras of...

The aim of this paper is to define cubic Dirac operators for colour Lie algebras. We give a necessary and sufficient condition construct algebra from an $\epsilon$-orthogonal representation $\epsilon$-quadratic algebra. This used prove strange Freudenthal-de Vries formula basic algebras as well Parthasarathy calculate the cohomology induced by operator, analogously algebraic Vogan conjecture pr...

In this paper we present the results of computation of cohomology for some Lie (super)algebras of Hamiltonian vector fields and related algebras. At present, the full cohomology rings for these algebras are not known even for the low dimensional vector fields. The partial “experimental” results may give some hints for solution of the whole problem. The computations have been carried out with th...

suppose $pi:mathcal{a}rightarrow mathcal{b}$ is a surjective unital $ast$-homomorphism between c*-algebras $mathcal{a}$ and $mathcal{b}$, and $0leq aleq1$ with $ain  mathcal{a}$. we give a sufficient condition that ensures there is a proection $pin mathcal{a}$ such that $pi left( pright) =pi left( aright) $. an easy consequence is a result of [l. g. brown and g. k. pedersen, c*-algebras of real...

Starting from the well-known quantum Miura-like transformation for the non simply-laced Lie algebras B N , we give an explicit construction of the Casimir W B 3 algebras. We reserve the notation WB N for the Casimir W algebras of type W 1 2) which contains one fermionic field. It is seen that W B 3 algebra is closed and associative for all values of the central charge c.